Three months before the 1963 March on Washington, whose 50th anniversary falls this week, officials in Birmingham, Ala., opened fire hoses and loosed dogs on civil rights protesters. Two months before the march, the civil rights organizer Medgar Evers was murdered outside his home in Jackson, Miss. And a few weeks after the Rev. Martin Luther King Jr.’s “I Have Dream Speech” echoed down the Washington Mall, a bomb ripped open Birmingham’s 16th Street Baptist Church, killing four little girls.

Fifty years later, race is still in the headlines; indeed, the “post-racial” presidency of President Barack Obama has (predictably) given us more race-related controversy than the last two administrations combined. Some of these debates are essentially trivial, churned up by a “no, you’re the racist” grievance factory that runs day and night on cable news. But others — on voting rights, affirmative action, stop-and-frisk, etc. — are serious and weighty whatever side you take.

So America was divided by race in 1963 and it is divided by race today. But it is not divided in anything like the same way. And the case for optimism about racial polarization starts with what the fire hoses and bombs of ’63 signify about the difference between the civil rights era and our own.

Then, the major issue facing black America was entirely zero-sum: For King to win, Bull Connor had to lose. There was no potential common ground so long as segregation lasted. Jim Crow had to perish outright for African-Americans to move forward as Americans. And their white supremacist oppressors knew it, which is why they turned to state-sponsored violence and state-sanctioned terrorism to defend their system and way of life.

Today our polarized politics may encourage a zero-sum attitude, but the underlying realities do not. George Zimmerman is not a half-Hispanic Byron De La Beckwith. Voter ID laws are not Jim Crow come again. And the thread of white identity politics running through Obama-era conservatism is just that — a sense of resentment and grievance, not a supremacist ideology reborn.

The interests of white and black Americans do not always align, any more than the interests of Ohioans and Californians, or senior citizens and younger Americans, or the college-educated and the working-class. But there is vastly more room to work through major problems together than there was in the Alabama and Mississippi of 1963.

How so? Well, start with that most reliably controversial of race-related issues: criminal justice, where America’s drug laws and incarceration rates are often cited by civil rights activists as an example of how structural racism threatens to create a “new Jim Crow.”

Except that while the actual Jim Crow invariably pitted white, Southern, conservative politicians against civil rights activists, today criminal justice is a place where many conservative politicians have embraced activists’ priorities instead. Attorney General Eric Holder’s recent proposals for sentencing reform, for instance, followed a path blazed by Rick Perry in Texas a decade ago. In the Senate, the conservative Republican with the closest ties to the states-rights ideology that once justified segregation, Rand Paul, is also the loudest voice in support of reconsidering the War on Drugs.

Likewise in education policy, another longstanding racial flash point. There the older battles over integration and busing have mostly given way to a debate about competition and teacher standards in which conservative states are often laboratories for reform. From Chris Christie’s New Jersey to Perry’s Texas (which does a better job educating minority students than many liberal states), the politics of education increasingly produces cross-racial alliances and intraparty debates that look nothing like the civil-rights era divides.

Meanwhile, in the broader socioeconomic landscape, the big story of the last generation in American life is that problems that were seen as specifically “black problems” in the 1970s and 1980s — persistent unemployment, especially for men, family breakdown and social disarray — are now problems affecting the pan-ethnic working class.

Neither party currently has an agenda that’s well tailored to this challenge. But because the problems themselves increasingly cut across racial lines, a successful political response from either party would probably tend to reduce racial polarization — winning more minority votes for the Republicans or more working-class whites for the Democrats — and encourage socioeconomic solidarity instead.

Obviously, no such agenda could emerge, and the Obama race wars could continue indefinitely — with the Republican Party as a vehicle for white identity politics and the Democratic Party as a vehicle for ethnic patronage, with voter ID laws and affirmative action as permanent flash points, and with less racially polarizing issues shunted to the side.

But unlike the racial conflict of 50 years ago, there is nothing necessary about this kind of division. And this week of all weeks, it’s fitting to have a different dream.